TV or full screen aspect ratio is 4:3, meaning the screen has 3 units of height for every 4 units of width. A 48-inch wide screen is 36 inches high if it is in 4:3 aspect ratio. Widescreen format is 16:9, so a 48-inch wide television would be only 27 inches high. The wider viewing area allows panoramic landscapes, which the television aspect ratio does not permit.
Playing a full screen DVD on a widescreen TV results in a picture too narrow for the screen. To compensate, black bars fill the unused space on either side of the picture. Likewise, playing a widescreen DVD on a standard screen may require black bars above and below the image. This is called "Letterboxing." Some widescreen movies are reformatted for TV aspect ratio using "Pan and scan" technique. This format uses 4:3 aspect ratio, which cuts off the too-wide sides of the image. The presented view pans across the existing picture in some scenes, revealing the relevant image in smaller amounts as if a camera is moving across the scene.
Some people prefer full screen viewing to avoid the distraction of letterboxing on a TV screen, while others dislike the "pan and scan" version because it presents the movie in a view different from its director's and editor's intent. Whenever possible, try to view films that were shot in 16:9 aspect ratio on a widescreen and those shot in 4:3 on a standard screen to get the truest picture.
If you have a DVD that offers both formats, it was likely shot in widescreen format, and the full screen format is "pan and scan." For a picture true to the original, choose widescreen; for an image better suited to a standard TV without letterboxing, choose the full screen version.